Updated 12/13/16 with new solution; see Edit comment.
Just posting a potential fix if anyone else is running into the same problem and searching for answers.
XFX RX 480 RS 8 GB, latest driver as of 12/07/16
LG Electronics Ultrawide 34UC79G-B using Displayport
2560x1080@144 Hz, Freesync on in AMD control panel and in monitor settings
Description of issue:
Black screen intermittently in fullscreen 3D applications where the application does not crash or otherwise lock up, but will resume normally within several seconds.
Reproduction of issue:
Monitor will black out intermittently during intense 3D application usage. Multiple occurrences during stress testing and during normal 3D application usage.
See link at bottom for video of issue.
Turning off Displayport 1.2 support in the monitor's settings using the OSD resolved the issue.
Changing the display color depth to 6 bpc (from 8) in Radeon Additional Settings has resolved the issue completely with Display Port 1.2/Freesync enabled.
Link to video of issue (from another user with the same problem): LG 34UC88 - Displayport Freesync Issues - Disconnects - Blank Screen and sound cutting out - Vid 1 - YouTube